How the Higgs Field Works (with math)

This set of articles explains how the Higgs field gives mass to other particles, and some details about the Higgs particle.

These articles require the kind of math that you’d come across in advanced pre-university or beginning university settings: algebra, cosines and sines, a little calculus (though most of that can be skirted) and a little familiarity with simple physics concepts: energy, oscillations, waves.  Some of this stuff is reviewed in the Particles and Fields articles in any case.

1. The Basic Idea (of how the Higgs field gives mass to other particles.)

2. Why The Higgs Field Becomes Non-Zero, unlike other fields.

3. How the Higgs Particle Arises, as a quantum of the waves in the Higgs field as it oscillates around its non-zero equilibrium value.

4. Why the Higgs Field is Necessary (why in our universe, with its weak nuclear force, the electron can’t have a mass without it.)

Before reading these articles you should first read through my set of articles on Particles and Fields, which are at the same level, and are intended to lead directly to this set.


31 thoughts on “How the Higgs Field Works (with math)”

  1. Fantastic – this is just what I was hopings for !! Other than a brief mention in the introduction to Lisa Randall’s book, information has been sketchy and not meant for those with some training in physics. I started out as a Physics major (45 years ago) but then discovered computers and my life’s direction took a new turn, but I’ve never lost my fascination with (and love of) physics (and now cosmology) and have kept up as best I could over time. It just gets better and better 🙂 Also great exercise for my brain – they do say ‘use it or lose it’. I look forward to lots of ‘use’ as I follow your articles – LOL !!

  2. Thank you for the great description of the Higgs mechanism. I have a question. You described two different kinds of field equations, Class 0 (for massless particles) and Class 1 (for massive particles). Class 0 is the traditional wave equation, which is easily seen to be Lorentz invariant. But is the Class 1 wave equation you described also Lorentz invariant?

  3. I think I answered my own question. Your Class 1 equation is the Klein-Gordon equation, which of course is Lorentz invariant, provided the field transforms like a scalar.

  4. Ted talks has Dr Harry Cliff say that the particular strength of the Higgs fileld is a surprise as it should be either zero or ginormous although both are incompatible with the existence of our universe . He says a large number of other things in the talk that sound quite outlandish such as the LHC result was a huge surprise as they should have found other particles produced with it but they didn’t and that physicists have tried and failed to explain the particular strength of the Higgs field for decades and that “his” group at CERN published paper afte paper after the first run that concluded that That run had failed to find any support for the “most elegant” theory namely string theory or its alternative – the multiverse theory.

    Is this man really a player or just a trouble maker? Is quantum mechanics and general relativity leading us to God as he seems to suggest? Has string theory led to any prediction that helps us apart from the theory that it has a ginormous number of theories in it
    . ? Help ! 😳😳😳😳🙃🙃🙃

  5. ” I think that the De Broogle matter-waves and David Bohms pilot-waves are waves in the Higgs field and it is the Higgs field that tells the matter particles how they have to move in a gravitational field and in the double-slit experiment. (electrons get their mass after the slits according to the interference in Higgs waves)

    For example in QED calculations and in the double-slit experiment it is not the electrons that are taking all the possible paths , it is only the waves in the Higgs field that travels all the paths.

    That means that Niels Bohrs principle of complementarity where a particle is both a particle and a wave at the same time is not needed any longer. Higgs field gives electrons their mass and the waves in the Higgs field tell them how to moove.

    At the same time we can notice that we dont need Einsteins 4:th room-time dimension any longer , because it is only a mathematical construction. The real physical reality are waves and structures in the Higgs field”

  6. Well, I have some thought s about gravity and it is very stupid, that might explain the cause of gravity:
    * mass comes from Highs Bosson,
    * gravity is due to mass.
    So, could that be reasons to look for gravity explained in that field…
    There is just enough phenomenon s to finally explain it… Or to come pretty had damn close…
    Time locally might be discontinuous and globally continuous…
    Time to introduce layers of space time and Fuzzy logic in order to create one cosisyen theory…

  7. Particularly, years of instructional excessive-stakes testing robs many college
    students of the one ingredient important to actual studying:
    being keen to take risks and to fail .

    With an odd mathematical proof the World could seem unusual and incomprehensible.

  8. Dear Professor Strassler, I see that Harry Cliff has said the Higgs field is 10^16 times smaller than predicted. Could you provide a more accurate figure including error margins? I am an enthusiastic, amateur physicist and these discrepancies fascinate me.

  9. I do not know about field and solution to simultaneous field equations. But when field follows the curvature of space, mass of the field disappears. But when the curvature of space is straightened out, the field has mass.


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